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First-principles study of structural, electronic, and optical properties of ZnSnO3
Solid State Communications 149 (2009) 1849–1852
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
First-principles study of structural, electronic, and optical properties of ZnSnO3 Hai Wang a , Haitao Huang a,∗ , Biao Wang b a
Department of Applied Physics and Materials Research Center, The Hong Kong Polytechnic University, Hong Kong, China
b
School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275, China
article
info
Article history: Received 15 December 2008 Received in revised form 13 May 2009 Accepted 1 July 2009 by S. Tarucha Available online 15 July 2009 PACS: 71.15.Mb 78.20.Ci 77.84.Dy
abstract The structural, electronic, and optical properties of ZnSnO3 were investigated using density functional theory within the generalized gradient approximation. The structure parameters obtained agree well with the experimental results. The electronic structures indicate that ZnSnO3 is a semiconductor with a direct band gap of 1.0 eV. The calculated optical spectra can be assigned to contributions of the interband transitions from valence band O 2p levels to conduction band Sn 5s levels or higher conduction band Zn 3d levels in the low-energy region, and from O 2p to Sn 5p or Zn 4p conduction band in the high-energy region. © 2009 Elsevier Ltd. All rights reserved.
Keywords: A. Ferroelectrics D. Electronic band structure D. Optical properties
1. Introduction It is well known that materials properties are closely related to their crystal structures and the structure-property relationships are extensively used to guide researchers in the design of new high-performance materials. For example, materials with a noncentrosymmetric structure tend to have ferroelectricity and second-order nonlinear optical behavior, and therefore are of special interest in materials chemistry [1]. Noncentrosymmetric materials with an R3c structure have attracted increasing attention due their importance in fundamental physics and technical applications. For example, LiNbO3 [2] is a promising nonlinear optical material and BiFeO3 [3,4] is a multiferroic materials. LaAlO3 with R3c structure shows excellent dielectric properties and can be used as gate dielectrics [5] due to the fact that rare-earth aluminates with a rhombohedral structure exhibit larger permittivities than those with an orthorhombic structure [6]. Recently, polycrystalline zinc stannate (ZnSnO3 ) has been synthesized [7] by a solid-state reaction under high pressure (7 GPa) at elevated temperature (1000 ◦ C). X-Ray diffraction (XRD) results show that ZnSnO3 crystallizes with a noncentrosymmetric R3c structure, which is the same as that of a polar oxide LiNbO3 [8–10]. Due to the lack of inversion symmetry, this type of crystals displays
∗
Corresponding author. Tel.: +86 852 27665694. E-mail address: [email protected] (H. Huang).
0038-1098/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2009.07.009
ferroelectricity, the Pockels effect, piezoelectric effect, photoelasticity, and nonlinear optical polarizability. Therefore, ZnSnO3 is a promising candidate for multifunctional applications. Furthermore, the Zn–Sn–O systems are transparent conducting oxides [11]. To the best of our knowledge, there is no theoretical study on this compound so far. 2. Method In this work, we have calculated and investigated the structural, electronic, and optical properties of ZnSnO3 by using an accurate full-potential linearized augmented plane-wave method (FPLAPW) as implemented in WIEN2k code [12]. Exchange and correlation effects are treated within the generalized gradient approximation (GGA) [13]. It is known that the dielectric function is connected with the electronic response. The imaginary part of the dielectric function ε2 (ω) is calculated from the momentum matrix elements between the occupied and unoccupied wave functions and given by [14]
ε2 (ω) =
V e2 2π ¯
hm2
Z ω
2
d3 k
X
|hkn|p|kn0 i|2
nn0
× f (kn)(1 − f (kn0 ))δ(Ekn − Ekn0 − h¯ ω)
(1)
where h¯ ω is the energy of the incident phonon, p is the momentum operator −ih¯ ∇, |kni is a crystal wave function, and f (kn) is the Fermi–Dirac distribution function. The real part of the dielectric
1850
H. Wang et al. / Solid State Communications 149 (2009) 1849–1852
a
c
b
Fig. 1. Projection of ZnSnO3 crystal structure on (a) (110), (b) (101), and (c) (011) planes. Table 1 3
Experimental and calculated lattice constants a and c (Å), Volume V (Å ) and atomic fractional coordinates, where the hexagonal structure was used.
a
Exp. Cal.b a b
a
c
V
Zn (0, 0, z)
O (x, y, z)
5.2622 5. 3441
14.0026 14.2206
111.9 117.2
0.2859 0. 2827
0.0405, 0.3500, 0.0709 0.0357, 0.3587, 0.0689
Reference [7]. Present work.
function ε1 (ω) is evaluated from imaginary part ε2 (ω) by the Kramer–Kronig transformation. Optical constants, such as, the energy dependence of absorption coefficient, refractive index, extinction coefficient, energy-loss spectrum, and reflectivity can be derived from ε2 (ω) and ε1 (ω) [14]. ZnSnO3 crystal has a rhombohedral crystal symmetry and belongs to the R3c (C 3v) crystallographic point group, where the Sn atom sits at the origin (Fig. 1). The muffin–tin sphere radii are 2.0, 1.9, and 1.6 au for Zn, Sn, and O atoms, respectively. For controlling the size of basis set for the wave functions, Rmt Kmax was set to 7.0, and the well-converged basis sets consist of about 1078 LAPW functions and 88 local orbits chosen for O 2s, O 2p, Zn 3s, Zn 3p, Zn 3d, Sn 5s, and Sn 5p states. Integrations in the reciprocal space were performed by using the tetrahedron method [15] and a 10 × 10 × 10 mesh was used to represent 110 k-points in the irreducible wedge of the Brillouin zone (BZ). The spin–orbit coupling was not taken into in our calculation since it has a minor influence on the optical properties for ferroelectric and semiconducting materials [16,17]. 3. Results and discussion First of all, we performed full structural optimization of ZnSnO3 with the calculated structural parameters listed in Table 1. The calculated lattice constants (a, c ) are 1.6% larger than the experimental values, while theoretical equilibrium volume is about 4.8% larger. In our previous results, it was also found that GGA significantly overestimate (2%–5% or more) the equilibrium volume of materials synthesized at high-pressure, such as Bi2 ZnTiO6 [18]. Shown in Fig. 2 is the calculated band structure of ZnSnO3 along the high-symmetry directions in the BZ. Total and partial density of states (DOS) are given in Fig. 3. In the valence band (VB), the energy band at the lowest region of [−18.4, −15.3] eV is mainly occupied by O 2s state mixed with some Sn 4d states. The bands at about [−8.1, −5.5] eV are due to Sn 5s state mixed with some O 2p and Zn 3d states, while in the region [−5.5, −3.4] eV, the Zn 3d is dominant with O 2p and little Sn 5p states. In the top of the VB ([−3.4, 0] eV), the O 2p state is dominant, which is also mixed with
some Zn 3d and little Sn 4d states, indicating strong hybridization between them. The conduction band (CB) region of [1, 5.5] eV is dominated by Sn 5s and Zn 4s states, while Sn 5p is dominant over Zn 4p state when the energy is larger than 5.5 eV. It is noted that Zn PDOS is so small that can be ignored for energies lower than 5.5 eV. Therefore, the electronic properties of ZnSnO3 should be controlled by Sn 5s and O 2p states. Both the top of the VB and bottom of the CB are located at Γ -point. Hence, a direct band gap with 1.0 eV is formed, indicating ZnSnO3 is a semiconductor. It should be noted that there is no experimental band gap value to compare and DFT usually underestimates the band gap of semiconductor solids. It is well known that the electronic structure of the transitionmetal oxide with d0 electronic configuration in ABO3 -type perovskite structure (e.g., SrTiO3 , KNbO3 , or NaTaO3 ) is generally determined by the d orbital of the transition-metal ion and the O 2p level [19,20]. For the metal oxide containing metal ion with d10 electronic configuration (e.g., In3+ , Ge4+ , or Sb5+ ), however, the conduction band is not derived from its (n − 1)d orbital but the ns orbital. Theoretical calculation indicates that the d band from the (n − 1)d orbitals is deep inside the valence band. These are the common features [21] of band structures for metal oxides with octahedrally coordinated d10 configuration, such as CdSnO3 , CdSnO3 and KSbO3 , etc. Our results confirmed that these rules are valid for the case of ZnSnO3 in perovskite R3c structure. In addition to the electronic structure, we have also calculated the complex dielectric constant and the optical properties (including refractive index, extinction coefficient, energy-loss spectrum, and reflectivity) using the OPTIC package [22] of WIEN2k. The scissor approximate technique (SAT) is widely used in the calculation of dielectric function of oxides such as BaTiO3 [20]. However, we didn’t use this technique due to the lack of experimental band gap value of ZnSnO3 . The imaginary part ε2 (ω) and real part ε1 (ω) of the dielectric function of ZnSnO3 are shown in Fig. 4, where the solid and dotted lines represent the results along the direction of xx and zz, respectively. There are about 11 peaks in the imaginary part of the dielectric function, more than that in BaTiO3 [20]. The first peak A (about 2.5 eV)
H. Wang et al. / Solid State Communications 149 (2009) 1849–1852
a
8.0
1851
b
7.0 6.0 5.0 4.0 3.0 2.0
Energy (eV)
1.0 0.0
E
-1.0 -2.0 -3.0 -4.0 -5.0 -6.0 -7.0 -8.0 -9.0 -10.0
G
Z
L
G
F
Fig. 2. (a) Band structure along the high-symmetry directions and (b) the first BZ of ZnSnO3 with high-symmetry points, G (0, 0, 0), Z (0.5, 0.5, 0.5), L (0.0, 0.5, 0.0), and F (0.5, 0.5, 0.0). The symbols a*, b*, and c* denote the reciprocal vectors.
Fig. 4. The imaginary part ε2 (ω) and real part ε1 (ω) of the dielectric function of ZnSnO3 . The solid and dotted lines represent the results along the polarization direction of xx and zz, respectively.
Fig. 3. Total and partial density of states in ZnSnO3 . The top of the valence band is set at 0 eV.
corresponds mainly to the transition from O 2p VB to Sn 5s CB. Peaks B (4.93 eV) and C (5.50 eV) correspond to the transition from O 2p or Zn 3d VB to Sn 5s CB. Peaks D (6.66 eV), E (7.07 eV), F (7.70 eV), and G (7.99 eV) correspond mainly to the transitions from O 2p VB to Sn 5s or Zn 4s high-energy CB. The optical properties of critical peaks of H (9.50 eV) and I (11.20 eV) are ascribed to the transitions of O 2p levels to Sn 5s and Zn 4s CB (or O 2p and Zn 3d CB to Sn 5p and Zn 4p CB). Peaks J (14.93 eV) and K (15.99 eV) correspond mainly to the transitions from O 2p VB to Sn 5p or Zn 4p high-energy CB. There are no clear-cut structures for ε2 (ω) above 16 eV, because the coupling of oscillator strength between VB and CB vanishes [23]. It is noted that a peak in ε2 (ω) does not correspond to a single interband transition since many
direct or indirect transitions may be found in the band structure with an energy corresponding to the same peak. Fig. 5(a)–(e) show the calculated results on the energy dependence of absorption coefficient, refractive index (n), extinction coefficient, energy-loss spectrum, and reflectivity, respectively. In our calculation, we used Gaussian smearing of 0.1 eV. It can be observed that the optical spectra are quite similar along two different directions over a wide energy range except in some energy windows (about [6, 11] and [27, 29] eV) where the difference between the xx and zz tensor components are quite large. Similar behaviors are also found in dielectric functions. For the absorption coefficient calculation, we only consider the eigen-absorption, while the polarized absorption was not taken into consideration since it has minor influence on absorption coefficient [24]. The absorption spectrum, started at 1.0 eV, is very large (about 106 cm−1 ) and decreases rapidly in the low-energy region. The refractive index in the region of [6, 11] eV shows a substantial change from
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H. Wang et al. / Solid State Communications 149 (2009) 1849–1852
top of the valence band and the bottom of the conduction band are decided by O 2p and Sn 5s states, respectively, and that ZnSnO3 presented a direct band gap (1.0 eV) located at Γ -point. Finally, the complex dielectric function and optical constants (such as, absorption spectrum, refractive index, extinction coefficient, reflectivity, and energy-loss spectrum) were obtained and discussed in detail. Our results suggested that ZnSnO3 is a promising transparent semiconductor and photocatalyst. Acknowledgements This work was supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region (Project: PolyU 5171/07E) and the Hong Kong Polytechnic University (Project Nos.: G-YH07 and G-YF71). References
Fig. 5. Calculated optical constants of rhombohedral ZnSnO3 . (a) Absorption spectrum (105 /cm), (b) refractive index, (c) extinction coefficient, (d) energy-loss spectrum, and (e) reflectivity. The solid and dotted lines represent the result along the polarization direction of xx and zz, respectively.
basically isotropic to anisotropic accompanied by a change of the sign of birefringence 1n = nzz − nxx from uniaxial negative to uniaxial positive. At an energy of 6.90 eV, a large birefringence of 1n = −0.2 can be found. This may be caused by the fact that the optical transition along xx polarization direction is easier than that in zz direction. In the range of 0–6.0 eV, the reflectivity was lower than 25%, which indicates that ZnSnO3 is transparent for phonon energy less than 6.0 eV. The energy-loss spectrum is related to the energy loss of a fast electron traversing in the material and is usually large at the plasma energy [25]. The peaks of the spectrum calculated by our FP-LAPW are at about 23 eV. This corresponds to a rapid decrease of reflectance in Fig. 5(e). This process is associated with transitions from the occupied Sn 4d and O 2s bands, lying below the VB, to an empty CB. 4. Conclusion We have calculated the structural, electronic and optical properties of ZnSnO3 using the FP-LAPW method in a wide energy range. Our structural parameters are in good agreement with the experimental values. The electronic structures revealed that the
[1] P.S. Halasyamani, K.R. Poeppelmeier, Chem. Mater. 10 (1998) 2753. [2] Y.P. Guo, K. Kakimoto, H. Ohsato, Appl. Phys. Lett. 85 (2004) 4121. [3] S.Y. Yang, F. Zavaliche, L. Mohaddes-Ardabili, V. Vaithyanathan, D.G. Schlom, Y.J. Lee, Y.H. Chu, M.P. Cruz, Q. Zhan, T. Zhao, R. Ramesh, Appl. Phys. Lett. 87 (2005) 102903. [4] S. Fujino, M. Murakami, V. Anbusathaiah, S.H. Lim, V. Nagarajan, C.J. Fennie, M. Wuttig, L. Salamanca-Riba, I. Takeuchi, Appl. Phys. Lett. 92 (2008) 202904. [5] S.G. Lim, S. Kriventsov, T.N. Jackson, J.H. Haeni, D.G. Schlom, A.M. Balbashov, R. Uecker, P. Reiche, J.L. Freeouf, G. Lucovsky, J. Appl. Phys. 91 (2002) 4500. [6] S.Y. Cho, I.T. Kim, K.S. Hong, J. Mater. Res. 14 (1999) 114. [7] Y. Inaguma, M. Yoshida, T. Katsumata, J. Am. Chem. Soc. 130 (2008) 6704. [8] S.C. Abrahams, J.M. Reddy, J.L. Bernstein, J. Phys. Chem. Solids 27 (1966) 997. [9] R. Hsu, E.N. Maslen, D. du Boulay, N. Ishizawa, Acta Crystallogr. B 53 (1997) 420. [10] H. Megaw, Acta Crystallogr. A 24 (1968) 583. [11] J.D. Perkins, J.A. del Cueto, J.L. Alleman, C. Warmsingh, B.M. Keyes, L.M. Gedvilas, P.A. Parilla, B. To, D.W. Readey, D.S. Ginley, Thin Solid Films 411 (2002) 152. [12] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2K, Technical University of Vienna, Austria, 2001, ISBN 3-9501031-1-2. [13] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [14] S. Saha, T.P. Sinha, A. Mookerjee, Phys. Rev. B 62 (2000) 8828. [15] P.E. Blohl, O. Jepsen, O.K. Andersen, Phys. Rev. B 49 (1994) 16223. [16] S. Sharma, C. Ambrosch-Draxl, M.A. Khan, P. Blaha, S. Auluck, Phys. Rev. B 60 (1999) 8610. [17] R. Ahuja, O. Eriksson, B. Johansson, S. Auluck, J.M. Wills, Phys. Rev. B 54 (1996) 10419. [18] H. Wang, H. Huang, W. Lu, H.L.W. Chan, B. Wang, C.H. Woo, J. Appl. Phys. 105 (2009) 053713. [19] D.E. Scaife, Sol. Energy 25 (1980) 41. [20] M.Q. Cai, Z. Yin, M.S. Zhang, Appl. Phys. Lett. 83 (2003) 2805. [21] W.F. Zhang, J.W. Tang, J.H. Ye, J. Mater. Res. 22 (2007) 1859. [22] C. Ambrosch-Draxl, J.A. Majewski, P. Vogl, G. Leising, Phys. Rev. B 51 (1995) 9668. [23] S. Kohiki, M. Arai, H. Yoshikawa, S. Fukushima, Phys. Rev. B 57 (1998) 14572. [24] C. Persson, R. Ahuja, A.F. da Silva, B. Johansson, J. Cryst. Growth 231 (2001) 407. [25] M. Xu, S.Y. Wang, G. Yin, J. Li, Y.X. Zheng, L.Y. Chen, Y. Jia, Appl. Phys. Lett. 89 (2006) 151908.
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
First-principles study of structural, electronic, and optical properties of ZnSnO3 Hai Wang a , Haitao Huang a,∗ , Biao Wang b a
Department of Applied Physics and Materials Research Center, The Hong Kong Polytechnic University, Hong Kong, China
b
School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275, China
article
info
Article history: Received 15 December 2008 Received in revised form 13 May 2009 Accepted 1 July 2009 by S. Tarucha Available online 15 July 2009 PACS: 71.15.Mb 78.20.Ci 77.84.Dy
abstract The structural, electronic, and optical properties of ZnSnO3 were investigated using density functional theory within the generalized gradient approximation. The structure parameters obtained agree well with the experimental results. The electronic structures indicate that ZnSnO3 is a semiconductor with a direct band gap of 1.0 eV. The calculated optical spectra can be assigned to contributions of the interband transitions from valence band O 2p levels to conduction band Sn 5s levels or higher conduction band Zn 3d levels in the low-energy region, and from O 2p to Sn 5p or Zn 4p conduction band in the high-energy region. © 2009 Elsevier Ltd. All rights reserved.
Keywords: A. Ferroelectrics D. Electronic band structure D. Optical properties
1. Introduction It is well known that materials properties are closely related to their crystal structures and the structure-property relationships are extensively used to guide researchers in the design of new high-performance materials. For example, materials with a noncentrosymmetric structure tend to have ferroelectricity and second-order nonlinear optical behavior, and therefore are of special interest in materials chemistry [1]. Noncentrosymmetric materials with an R3c structure have attracted increasing attention due their importance in fundamental physics and technical applications. For example, LiNbO3 [2] is a promising nonlinear optical material and BiFeO3 [3,4] is a multiferroic materials. LaAlO3 with R3c structure shows excellent dielectric properties and can be used as gate dielectrics [5] due to the fact that rare-earth aluminates with a rhombohedral structure exhibit larger permittivities than those with an orthorhombic structure [6]. Recently, polycrystalline zinc stannate (ZnSnO3 ) has been synthesized [7] by a solid-state reaction under high pressure (7 GPa) at elevated temperature (1000 ◦ C). X-Ray diffraction (XRD) results show that ZnSnO3 crystallizes with a noncentrosymmetric R3c structure, which is the same as that of a polar oxide LiNbO3 [8–10]. Due to the lack of inversion symmetry, this type of crystals displays
∗
Corresponding author. Tel.: +86 852 27665694. E-mail address: [email protected] (H. Huang).
0038-1098/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2009.07.009
ferroelectricity, the Pockels effect, piezoelectric effect, photoelasticity, and nonlinear optical polarizability. Therefore, ZnSnO3 is a promising candidate for multifunctional applications. Furthermore, the Zn–Sn–O systems are transparent conducting oxides [11]. To the best of our knowledge, there is no theoretical study on this compound so far. 2. Method In this work, we have calculated and investigated the structural, electronic, and optical properties of ZnSnO3 by using an accurate full-potential linearized augmented plane-wave method (FPLAPW) as implemented in WIEN2k code [12]. Exchange and correlation effects are treated within the generalized gradient approximation (GGA) [13]. It is known that the dielectric function is connected with the electronic response. The imaginary part of the dielectric function ε2 (ω) is calculated from the momentum matrix elements between the occupied and unoccupied wave functions and given by [14]
ε2 (ω) =
V e2 2π ¯
hm2
Z ω
2
d3 k
X
|hkn|p|kn0 i|2
nn0
× f (kn)(1 − f (kn0 ))δ(Ekn − Ekn0 − h¯ ω)
(1)
where h¯ ω is the energy of the incident phonon, p is the momentum operator −ih¯ ∇, |kni is a crystal wave function, and f (kn) is the Fermi–Dirac distribution function. The real part of the dielectric
1850
H. Wang et al. / Solid State Communications 149 (2009) 1849–1852
a
c
b
Fig. 1. Projection of ZnSnO3 crystal structure on (a) (110), (b) (101), and (c) (011) planes. Table 1 3
Experimental and calculated lattice constants a and c (Å), Volume V (Å ) and atomic fractional coordinates, where the hexagonal structure was used.
a
Exp. Cal.b a b
a
c
V
Zn (0, 0, z)
O (x, y, z)
5.2622 5. 3441
14.0026 14.2206
111.9 117.2
0.2859 0. 2827
0.0405, 0.3500, 0.0709 0.0357, 0.3587, 0.0689
Reference [7]. Present work.
function ε1 (ω) is evaluated from imaginary part ε2 (ω) by the Kramer–Kronig transformation. Optical constants, such as, the energy dependence of absorption coefficient, refractive index, extinction coefficient, energy-loss spectrum, and reflectivity can be derived from ε2 (ω) and ε1 (ω) [14]. ZnSnO3 crystal has a rhombohedral crystal symmetry and belongs to the R3c (C 3v) crystallographic point group, where the Sn atom sits at the origin (Fig. 1). The muffin–tin sphere radii are 2.0, 1.9, and 1.6 au for Zn, Sn, and O atoms, respectively. For controlling the size of basis set for the wave functions, Rmt Kmax was set to 7.0, and the well-converged basis sets consist of about 1078 LAPW functions and 88 local orbits chosen for O 2s, O 2p, Zn 3s, Zn 3p, Zn 3d, Sn 5s, and Sn 5p states. Integrations in the reciprocal space were performed by using the tetrahedron method [15] and a 10 × 10 × 10 mesh was used to represent 110 k-points in the irreducible wedge of the Brillouin zone (BZ). The spin–orbit coupling was not taken into in our calculation since it has a minor influence on the optical properties for ferroelectric and semiconducting materials [16,17]. 3. Results and discussion First of all, we performed full structural optimization of ZnSnO3 with the calculated structural parameters listed in Table 1. The calculated lattice constants (a, c ) are 1.6% larger than the experimental values, while theoretical equilibrium volume is about 4.8% larger. In our previous results, it was also found that GGA significantly overestimate (2%–5% or more) the equilibrium volume of materials synthesized at high-pressure, such as Bi2 ZnTiO6 [18]. Shown in Fig. 2 is the calculated band structure of ZnSnO3 along the high-symmetry directions in the BZ. Total and partial density of states (DOS) are given in Fig. 3. In the valence band (VB), the energy band at the lowest region of [−18.4, −15.3] eV is mainly occupied by O 2s state mixed with some Sn 4d states. The bands at about [−8.1, −5.5] eV are due to Sn 5s state mixed with some O 2p and Zn 3d states, while in the region [−5.5, −3.4] eV, the Zn 3d is dominant with O 2p and little Sn 5p states. In the top of the VB ([−3.4, 0] eV), the O 2p state is dominant, which is also mixed with
some Zn 3d and little Sn 4d states, indicating strong hybridization between them. The conduction band (CB) region of [1, 5.5] eV is dominated by Sn 5s and Zn 4s states, while Sn 5p is dominant over Zn 4p state when the energy is larger than 5.5 eV. It is noted that Zn PDOS is so small that can be ignored for energies lower than 5.5 eV. Therefore, the electronic properties of ZnSnO3 should be controlled by Sn 5s and O 2p states. Both the top of the VB and bottom of the CB are located at Γ -point. Hence, a direct band gap with 1.0 eV is formed, indicating ZnSnO3 is a semiconductor. It should be noted that there is no experimental band gap value to compare and DFT usually underestimates the band gap of semiconductor solids. It is well known that the electronic structure of the transitionmetal oxide with d0 electronic configuration in ABO3 -type perovskite structure (e.g., SrTiO3 , KNbO3 , or NaTaO3 ) is generally determined by the d orbital of the transition-metal ion and the O 2p level [19,20]. For the metal oxide containing metal ion with d10 electronic configuration (e.g., In3+ , Ge4+ , or Sb5+ ), however, the conduction band is not derived from its (n − 1)d orbital but the ns orbital. Theoretical calculation indicates that the d band from the (n − 1)d orbitals is deep inside the valence band. These are the common features [21] of band structures for metal oxides with octahedrally coordinated d10 configuration, such as CdSnO3 , CdSnO3 and KSbO3 , etc. Our results confirmed that these rules are valid for the case of ZnSnO3 in perovskite R3c structure. In addition to the electronic structure, we have also calculated the complex dielectric constant and the optical properties (including refractive index, extinction coefficient, energy-loss spectrum, and reflectivity) using the OPTIC package [22] of WIEN2k. The scissor approximate technique (SAT) is widely used in the calculation of dielectric function of oxides such as BaTiO3 [20]. However, we didn’t use this technique due to the lack of experimental band gap value of ZnSnO3 . The imaginary part ε2 (ω) and real part ε1 (ω) of the dielectric function of ZnSnO3 are shown in Fig. 4, where the solid and dotted lines represent the results along the direction of xx and zz, respectively. There are about 11 peaks in the imaginary part of the dielectric function, more than that in BaTiO3 [20]. The first peak A (about 2.5 eV)
H. Wang et al. / Solid State Communications 149 (2009) 1849–1852
a
8.0
1851
b
7.0 6.0 5.0 4.0 3.0 2.0
Energy (eV)
1.0 0.0
E
-1.0 -2.0 -3.0 -4.0 -5.0 -6.0 -7.0 -8.0 -9.0 -10.0
G
Z
L
G
F
Fig. 2. (a) Band structure along the high-symmetry directions and (b) the first BZ of ZnSnO3 with high-symmetry points, G (0, 0, 0), Z (0.5, 0.5, 0.5), L (0.0, 0.5, 0.0), and F (0.5, 0.5, 0.0). The symbols a*, b*, and c* denote the reciprocal vectors.
Fig. 4. The imaginary part ε2 (ω) and real part ε1 (ω) of the dielectric function of ZnSnO3 . The solid and dotted lines represent the results along the polarization direction of xx and zz, respectively.
Fig. 3. Total and partial density of states in ZnSnO3 . The top of the valence band is set at 0 eV.
corresponds mainly to the transition from O 2p VB to Sn 5s CB. Peaks B (4.93 eV) and C (5.50 eV) correspond to the transition from O 2p or Zn 3d VB to Sn 5s CB. Peaks D (6.66 eV), E (7.07 eV), F (7.70 eV), and G (7.99 eV) correspond mainly to the transitions from O 2p VB to Sn 5s or Zn 4s high-energy CB. The optical properties of critical peaks of H (9.50 eV) and I (11.20 eV) are ascribed to the transitions of O 2p levels to Sn 5s and Zn 4s CB (or O 2p and Zn 3d CB to Sn 5p and Zn 4p CB). Peaks J (14.93 eV) and K (15.99 eV) correspond mainly to the transitions from O 2p VB to Sn 5p or Zn 4p high-energy CB. There are no clear-cut structures for ε2 (ω) above 16 eV, because the coupling of oscillator strength between VB and CB vanishes [23]. It is noted that a peak in ε2 (ω) does not correspond to a single interband transition since many
direct or indirect transitions may be found in the band structure with an energy corresponding to the same peak. Fig. 5(a)–(e) show the calculated results on the energy dependence of absorption coefficient, refractive index (n), extinction coefficient, energy-loss spectrum, and reflectivity, respectively. In our calculation, we used Gaussian smearing of 0.1 eV. It can be observed that the optical spectra are quite similar along two different directions over a wide energy range except in some energy windows (about [6, 11] and [27, 29] eV) where the difference between the xx and zz tensor components are quite large. Similar behaviors are also found in dielectric functions. For the absorption coefficient calculation, we only consider the eigen-absorption, while the polarized absorption was not taken into consideration since it has minor influence on absorption coefficient [24]. The absorption spectrum, started at 1.0 eV, is very large (about 106 cm−1 ) and decreases rapidly in the low-energy region. The refractive index in the region of [6, 11] eV shows a substantial change from
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top of the valence band and the bottom of the conduction band are decided by O 2p and Sn 5s states, respectively, and that ZnSnO3 presented a direct band gap (1.0 eV) located at Γ -point. Finally, the complex dielectric function and optical constants (such as, absorption spectrum, refractive index, extinction coefficient, reflectivity, and energy-loss spectrum) were obtained and discussed in detail. Our results suggested that ZnSnO3 is a promising transparent semiconductor and photocatalyst. Acknowledgements This work was supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region (Project: PolyU 5171/07E) and the Hong Kong Polytechnic University (Project Nos.: G-YH07 and G-YF71). References
Fig. 5. Calculated optical constants of rhombohedral ZnSnO3 . (a) Absorption spectrum (105 /cm), (b) refractive index, (c) extinction coefficient, (d) energy-loss spectrum, and (e) reflectivity. The solid and dotted lines represent the result along the polarization direction of xx and zz, respectively.
basically isotropic to anisotropic accompanied by a change of the sign of birefringence 1n = nzz − nxx from uniaxial negative to uniaxial positive. At an energy of 6.90 eV, a large birefringence of 1n = −0.2 can be found. This may be caused by the fact that the optical transition along xx polarization direction is easier than that in zz direction. In the range of 0–6.0 eV, the reflectivity was lower than 25%, which indicates that ZnSnO3 is transparent for phonon energy less than 6.0 eV. The energy-loss spectrum is related to the energy loss of a fast electron traversing in the material and is usually large at the plasma energy [25]. The peaks of the spectrum calculated by our FP-LAPW are at about 23 eV. This corresponds to a rapid decrease of reflectance in Fig. 5(e). This process is associated with transitions from the occupied Sn 4d and O 2s bands, lying below the VB, to an empty CB. 4. Conclusion We have calculated the structural, electronic and optical properties of ZnSnO3 using the FP-LAPW method in a wide energy range. Our structural parameters are in good agreement with the experimental values. The electronic structures revealed that the
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